function [ n, x, y, w, s ] = hexagon_lyness_rule09 ( )

%*****************************************************************************80
%
%% hexagon_lyness_rule09() sets the Lyness hexagon quadrature rule #09.
%
%  Licensing:
%
%    This code is distributed under the MIT license. 
%
%  Modified:
%
%    21 April 2019
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    James Lyness, Giovanni Monegato,
%    Quadrature rules for regions having regular hexagonal symmetry,
%    SIAM Journal on Numerical Analysis.
%    Volume 14 Number 2, April 1977, pages 283-295.
%
%  Output:
%
%    integer n, the number of points.
%
%    real x(n), y(n), the points.
%
%    real w(n), the weights.
%
%    integer s, the strength.
%
  n = 25;
  x = zeros ( n, 1 );
  y = zeros ( n, 1 );
  w = zeros ( n, 1 );
  
  x(1) = 0.0;
  y(1) = 0.0;
  w(1) = 0.08700554909480818;

  x(2) = 0.4877862138720692;
  y(2) = 0.0000000000000000;
  w(2) = 0.4317448087114455 / 6.0;
  for i = 3 : 7
    x(i) = cosd ( 60.0 ) * x(i-1) - sind ( 60.0 ) * y(i-1);
    y(i) = sind ( 60.0 ) * x(i-1) + cosd ( 60.0 ) * y(i-1);
    w(i) = w(i-1);
  end

  x(8) = 0.8207416571085249;
  y(8) = 0.0000000000000000;
  w(8) = 0.1650011139051992 / 6.0;
  for i = 9 : 13
    x(i) = cosd ( 60.0 ) * x(i-1) - sind ( 60.0 ) * y(i-1);
    y(i) = sind ( 60.0 ) * x(i-1) + cosd ( 60.0 ) * y(i-1);
    w(i) = w(i-1);
  end

  x(14) = 0.6684042062515772;
  y(14) = 0.3859033484068262;
  w(14) = 0.2714935927899824 / 6.0;
  for i = 15 : 19
    x(i) = cosd ( 60.0 ) * x(i-1) - sind ( 60.0 ) * y(i-1);
    y(i) = sind ( 60.0 ) * x(i-1) + cosd ( 60.0 ) * y(i-1);
    w(i) = w(i-1);
  end

  x(20) = 0.8295763593689278;
  y(20) = 0.4789561343950002;
  w(20) = 0.04475493549856469 / 6.0;
  for i = 21 : 25
    x(i) = cosd ( 60.0 ) * x(i-1) - sind ( 60.0 ) * y(i-1);
    y(i) = sind ( 60.0 ) * x(i-1) + cosd ( 60.0 ) * y(i-1);
    w(i) = w(i-1);
  end

  s = 11;

  return
end
